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Two campers leave their campsite at point A to go on a hike. Camper one heads east for 3 miles, then heads north 3 miles to point B. Camper two heads north for 2 miles and then east for 5 miles to point C. Referencing the triangle formed by A, B, and C, m∠B=108.43° and AC = 5.39. If the final distance between the two campers ends up being 2.24 miles, find the angle between the paths they traveled. Round the answer to the nearest degree.

A.23°
B.34°
C.37°
D.49°

Respuesta :

floresdaisy200oz7zy4
it's A
- Let the point where camper 1 heads north be D and the point where camper 2 heads 

Answer:23

Step-by-step explanation:

We need to find angle BAC

given angle B=108.43

AC=5.39

BC=2.24

Using Sine rule to get angle BAC

[tex]\frac{sinB}{AC}=\frac{sinA}{BC}[/tex]

[tex]sinA=2.24\times \frac{sin108.43}{5.39}[/tex]

[tex]sinA=0.3942[/tex]

[tex]A=sin^{-1}0.3942[/tex]

[tex]A=23.216\approx 23[/tex]

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